This is the whole question there is no initial investmentnt & Safari File Edit V

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This is the whole question there is no initial investmentnt

& Safari File Edit View History Bookmarks Window Help * 0 O BV C ng.cengage.com 4) 93% - Mon 8:20 O Rebecca Davenport + MINDTAP Assignment 11 - The Basics of Capital Budgeting Due Today at 11:59 PM PDT Cold Goose Metal Works Inc. is a small firm, and several of its managers are worried about how soon the firm will be able to recover its initial investment from Project Sigma's expected future cash flows. To answer this question, Cold Goose's CFO has asked that you compute the project's payback period using the following expected net cash flows and assuming that the cash flows are received evenly throughout each year. Complete the following table and compute the project's conventional payback period. For full credit, complete the entire table. am DOO • Year -6,000,000 Year 1 $2,400,000 Year 2 $5,100,000 Year 3 $2,100,000 Expected cash flow Cumulative cash flow Conventional payback period: N The conventional payback period ignores the time value of money, and this concerns Cold Goose's CFO. He has now asked you to compute Sigma's discounted payback period, assuming the company has a 7% cost of capital. Complete the following table and perform any necessary calculations. Round the discounted cash flow values to the nearest whole dollar, and the discounted payback period to the nearest two decimal places. For full credit, complete the entire table. Year o Year 1 Year 3 Year 2 Year 2 $5,100,000 -6,000,000 $2,400,000 $2,100,000 Cash flow Discounted cash flow Cumulative discounted cash flow . O . Discounted payback period: Which version of a project's payback period should the CFO use when evaluating Project Sigma, given its theoretical superiority? L 4000 AJAL 1 a 9x] - POW PEELEM

Explanation / Answer

TABLE 1 Soultion

To calculate Cumulative Cash Flows:

Year 0 = -6,000,000

Year 1= -6,000,000+2,4000,000 = - 3,600,000

Year 2= - 3,600,000 + 5,100,000 = 1,500,000

Year 3= 1,500,000+2,100,000 = 3,600,000

To calculate Conventional Payback Period ;

Inital Investment is 6,000,000

Year 1 return = 2,400,000

Remaining amount to recover after year 1 is (6,000,000 - 2,400,000) = 3,600,000

Year 2 Return is 5,100,000 ( which is higher than 3,600,000 )

Thus Fraction of Year 2 required to recover the remaining amount = 3,600,000 / 5,100,000 = 0.7058 = 0.71 (approx.)

Thus,

Conventional Payback Period = 1 + 0.71 = 1.71

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TABLE 2 Soultion

To calculate Discounted Cumulative Cash Flows: ( With R=7% )

For Given cost of capital ( R= 7%) , we have to take discounted future cash flow into account as follows :

Year 0 = -6,000,000

Year 1= -6,000,000+ 2,4000,000 / (1+ R)  = -6,000,000+ 2,4000,000 / (1+ 0.07) = -3,757,009.35

Year 2= -3,757,009.35 + 5,100,000 / (1+R)2 = 697,528.2

**Year 3= 697,528.2 + 2,100,000 / (1+R)3 = 2,411,754

To calculate Discounted Payback Period ;

Inital Investment is 6,000,000

Year 1 return = 2,400,000 / ( 1.07) = 2,242,991

Amount to be recovered after Year 1 = 6,000,000 - 2,242,991 = - 3,757,009

Year 2 return = 5,100,000 (1.07)2 = 4,454,538 ( Which is higher than - 3,757,009 )

Thus, fraction of Year 2 required to collect remaining initial cost = 3,757,009 / 4,454,538 = 0.8434 = 0.84 (approx)

Discounted Payback Period = 1 + 0.84= 1.84

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As we can see from above two scenarios , given it's theoritical superiorityCFO should use Regular(Convenional) payback period of 1.71 Years

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Also, the value discounted payback period fail to recognize is option 2 which is 2,411,755 ( Marked as ** in above explaination )

Explaining below again :

Year 0 = -6,000,000

Year 1= -6,000,000+ 2,4000,000 / (1+ R)  = -6,000,000+ 2,4000,000 / (1+ 0.07) = -3,757,009.35

Year 2= -3,757,009.35 + 5,100,000 / (1+R)2 = 697,528.2

**Year 3= 697,528.2 + 2,100,000 / (1+R)3 = 2,411,754

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